Selmer varieties for curves with CM Jacobians

Coates, John
Kim, Minhyong
Description
We study the Selmer variety associated to a canonical quotient of the $\Q_p$-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over $\Q$ whose Jacobian decomposes into a product of abelian varieties with complex multiplication. Elementary multi-variable Iwasawa theory is used to prove dimension bounds, which, in turn, lead to a new proof of Diophantine finiteness over $\Q$ for such curves.
Keywords
Mathematics - Number Theory, Mathematics - Algebraic Geometry, 11G30, 11R23